Skip to main content
SpringerLink
Log in

Semi-supervised Multi-view Clustering Based on Non-negative Matrix Factorization and Low-Rank Tensor Representation

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

Multi-view clustering methods aim to integrate the complementary information of different views to obtain accurate clustering results. However, the traditional multi-view clustering method is unsupervised which does not combine the label information. And in many practical applications, it is rare to provide fully labeled data, while partially labeled data is more common. In this paper, we propose a new semi-supervised multi-view clustering based on non-negative matrix factorization and low-rank tensor representation (LTMF) algorithm. Specifically, we first propose semi-supervised non-negative matrix factorization for multi-view to learn the low-rank representation of each view. Then, a 3-order tensor is constructed and further decomposed into a low-rank tensor and a sparse tensor. Finally, we perform spectral clustering on the low-rank tensor to obtain the final clustering result. Experiments are carried out on five different standard public datasets and the experimental results show that the clustering results of the proposed algorithm are better than other state-of-the-art comparison algorithms in ACC, NMI and Purity.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Notes

  1. https://www.cl.cam.ac.uk/research/dtg/attarchive/facedatabase.html.

  2. http://cvc.cs.yale.edu/cvc/projects/yalefaces/yalefaces.html.

  3. http://www.cs.columbia.edu/CAVE/software/softlib/coil-20.php.

  4. https://pgram.com/dataset/msrc-v1/.

References

  1. Xu D, Tian Y (2015) A comprehensive survey of clustering algorithms. Ann Data Sci 2(2):165–193

    Article  MathSciNet  Google Scholar 

  2. Kim E, Li H, Huang X (2012) A hierarchical image clustering cosegmentation framework. In: 2012 IEEE conference on computer vision and pattern recognition. IEEE, pp 686–693

  3. Mammone N, Ieracitano C, Adeli H, Bramanti A, Morabito FC (2018) Permutation Jaccard distance-based hierarchical clustering to estimate EEG network density modifications in mci subjects. IEEE Trans Neural Netw Learn Syst 29(10):5122–5135

    Article  Google Scholar 

  4. Bryant A, Cios K (2018) Rnn-dbscan: a density-based clustering algorithm using reverse nearest neighbor density estimates. IEEE Trans Knowl Data Eng 30(6):1109–1121

    Article  Google Scholar 

  5. Zhao L, Chen Z, Yang Y, Zou L, Wang ZJ (2019) ICFS clustering with multiple representatives for large data. IEEE Trans Neural Netw Learn Syst 30(3):728–738

    Article  Google Scholar 

  6. Bhatnagar V, Kaur S, Chakravarthy S (2014) Clustering data streams using grid-based synopsis. Knowl Inf Syst 41(1):127–152

    Article  Google Scholar 

  7. Zhang J, Feng X, Liu Z (2018) A grid-based clustering algorithm via load analysis for industrial internet of things. IEEE Access 6:13117–13128

    Article  Google Scholar 

  8. Vatsavai RR, Symons CT, Chandola V, Jun G (2011) Gx-means: a model-based divide and merge algorithm for geospatial image clustering. Procedia Comput Sci 4:186–195

    Article  Google Scholar 

  9. Slimen YB, Allio S, Jacques J (2018) Model-based co-clustering for functional data. Neurocomputing 291:97–108

    Article  MATH  Google Scholar 

  10. Han Y, Wang T (2021) Semi-supervised clustering for financial risk analysis. Neural Process Lett 53(5):3561–3572

    Article  MathSciNet  Google Scholar 

  11. Liu M, Nie L, Wang X, Tian Q, Chen B (2019) Online data organizer: micro-video categorization by structure-guided multimodal dictionary learning. IEEE Trans Image Process 28(3):1235–1247

    Article  MathSciNet  Google Scholar 

  12. Yang Z, Li Q, Liu W, Lv J (2020) Shared multi-view data representation for multi-domain event detection. IEEE Trans Pattern Anal Mach Intell 42(5):1243–1256

    Google Scholar 

  13. Wang H, Yang Y, Liu B, Fujita H (2019) A study of graph-based system for multi-view clustering. Knowl Based Syst 163:1009–1019

    Article  Google Scholar 

  14. Xiao Q, Du S, Zhang K, Song J, Huang Y (2022) Adaptive sparse graph learning for multi-view spectral clustering. Appl Intell 1–21

  15. Nie F, Wang X, Huang H (2014) Clustering and projected clustering with adaptive neighbors. In: Proceedings of the 20th ACM SIGKDD international conference on knowledge discovery and data mining, pp 977–986

  16. Kang Z, Pan H, Hoi SCH, Xu Z (2020) Robust graph learning from noisy data. IEEE Trans Cybern 50(5):1833–1843

    Article  Google Scholar 

  17. Huang Y, Xiao Q, Du S, Yu Y (2022) Multi-view clustering based on low-rank representation and adaptive graph learning. Neural Process Lett 54(1):265–283

    Article  Google Scholar 

  18. Shi J, Malik J (2000) Normalized cuts and image segmentation. IEEE Trans Pattern Anal Mach Intell 22(8):888–905

    Article  Google Scholar 

  19. Liu G, Lin Z, Yan S, Sun J, Yu Y, Ma Y (2013) Robust recovery of subspace structures by low-rank representation. IEEE Trans Pattern Anal Mach Intell 35(1):171–184

    Article  Google Scholar 

  20. Gao H, Nie F, Li X, Huang H (2015) Multi-view subspace clustering. In: 2015 IEEE international conference on computer vision, pp 4238–4246

  21. Zy Wang, Abhadiomhen SE, Zf Liu, Xj Shen, Wy Gao, Sy Li (2021) Multi-view intrinsic low-rank representation for robust face recognition and clustering. IET Image Proc 15(14):3573–3584

    Article  Google Scholar 

  22. Abhadiomhen SE, Wang Z, Shen X, Fan J (2021) Multiview common subspace clustering via coupled low rank representation. ACM Trans Intell Syst Technol 12(4):1–25

    Article  Google Scholar 

  23. Abhadiomhen SE, Wang Z, Shen X (2022) Coupled low rank representation and subspace clustering. Appl Intell 52(1):530–546

    Article  Google Scholar 

  24. Lee DD, Seung HS (2000) Algorithms for non-negative matrix factorization. In: Proceedings of the 13th international conference on neural information processing systems, pp 556–562

  25. Yang Z, Oja E (2010) Linear and nonlinear projective nonnegative matrix factorization. IEEE Trans Neural Netw 21(5):734–749

    Article  Google Scholar 

  26. Cai D, He X, Han J, Huang TS (2011) Graph regularized nonnegative matrix factorization for data representation. IEEE Trans Pattern Anal Mach Intell 33(8):1548–1560

    Article  Google Scholar 

  27. Li J, Zhou G, Qiu Y, Wang Y, Zhang Y, Xie S (2020) Deep graph regularized non-negative matrix factorization for multi-view clustering. Neurocomputing 390:108–116

    Article  Google Scholar 

  28. Liu H, Wu Z, Li X, Cai D, Huang TS (2012) Constrained nonnegative matrix factorization for image representation. IEEE Trans Pattern Anal Mach Intell 34(7):1299–1311

    Article  Google Scholar 

  29. Du S, Shi Y, Wang W, Ma M (2012) Graph regularized-based semi-supervised non-negative matrix factorization. Jisuanji Gongcheng yu Yingyong (Comput Eng Appl) 48(36):194–200

    Google Scholar 

  30. Liang N, Yang Z, Li Z, Xie S, Su CY (2020) Semi-supervised multi-view clustering with graph-regularized partially shared non-negative matrix factorization. Knowl Based Syst 190:105185

    Article  Google Scholar 

  31. Xing Z, Wen M, Peng J, Feng J (2021) Discriminative semi-supervised non-negative matrix factorization for data clustering. Eng Appl Artif Intell 103:104289

    Article  Google Scholar 

  32. Xie Y, Tao D, Zhang W, Liu Y, Zhang L, Qu Y (2018) On unifying multi-view self-representations for clustering by tensor multi-rank minimization. Int J Comput Vis 126(11):1157–1179

    Article  MathSciNet  MATH  Google Scholar 

  33. Du S, Liu B, Shan G, Shi Y, Wang W (2022) Enhanced tensor low-rank representation for clustering and denoising. Knowl Based Syst 243:108468

    Article  Google Scholar 

  34. Wu J, Lin Z, Zha H (2019) Essential tensor learning for multi-view spectral clustering. IEEE Trans Image Process 28(12):5910–5922

    Article  MathSciNet  MATH  Google Scholar 

  35. Du S, Shi Y, Shan G, Wang W, Ma Y (2021) Tensor low-rank sparse representation for tensor subspace learning. Neurocomputing 440:351–364

    Article  Google Scholar 

  36. Kilmer ME, Braman K, Hao N, Hoover RC (2013) Third-order tensors as operators on matrices: a theoretical and computational framework with applications in imaging. SIAM J Matrix Anal Appl 34(1):148–172

    Article  MathSciNet  MATH  Google Scholar 

  37. Du S, Xiao Q, Shi Y, Cucchiara R, Ma Y (2021) Unifying tensor factorization and tensor nuclear norm approaches for low-rank tensor completion. Neurocomputing 458:204–218

    Article  Google Scholar 

  38. Paatero P, Tapper U (1994) Positive matrix factorization: a non-negative factor model with optimal utilization of error estimates of data values. Environmetrics 5(2):111–126

    Article  Google Scholar 

  39. Shahid N, Kalofolias V, Bresson X, Bronstein M, Vandergheynst P (2015) Robust principal component analysis on graphs. In: 2015 IEEE international conference on computer vision, pp 2812–2820

  40. Lin Z, Liu R, Su Z (2011) Linearized alternating direction method with adaptive penalty for low-rank representation. In: Proceedings of the 24th international conference on neural information processing systems, pp 612–620

  41. Hu W, Tao D, Zhang W, Xie Y, Yang Y (2017) The twist tensor nuclear norm for video completion. IEEE Trans Neural Netw Learn Syst 28(12):2961–2973

    Article  MathSciNet  Google Scholar 

  42. Kang Z, Shi G, Huang S, Chen W, Pu X, Zhou JT, Xu Z (2020) Multi-graph fusion for multi-view spectral clustering. Knowl Based Syst 189:105102

    Article  Google Scholar 

  43. Sheng Y, Wang M, Wu T, Xu H (2019) Adaptive local learning regularized nonnegative matrix factorization for data clustering. Appl Intell 49(6):2151–2168

    Article  Google Scholar 

  44. Luong K, Nayak R (2022) Learning inter- and intra-manifolds for matrix factorization-based multi-aspect data clustering. IEEE Trans Knowl Data Eng 34(7):3349–3362

    Google Scholar 

Download references

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (No.61866033), the Gansu Provincial Department of Education University Teachers Innovation Fund Project (No.2023B-056), the Introduction of Talent Research Project of Northwest Minzu University (No. xbmuyjrc201904), the Fundamental Research Funds for the Central Universities (No. 31920220019, 31920220130), the Gansu Provincial First-class Discipline Program of Northwest Minzu University (No.11080305), the Leading Talent of National Ethnic Affairs Commission (NEAC), and the Young Talent of NEAC, and the Innovative Research Team of NEAC (2018) 98.

Author information

Authors and Affiliations

  1. College of Mathematics and Computer Science, Northwest Minzu University, Lanzhou, 730030, Gansu, China

    Yao Yu & Shiqiang Du

  2. Key Laboratory of China’s Ethnic Languages and Information Technology of Ministry of Education, Chinese National Information Technology Research Institute, Northwest Minzu University, Lanzhou, 730030, Gansu, China

    Baokai Liu, Shiqiang Du, Jinmei Song & Kaiwu Zhang

Authors
  1. Yao Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Baokai Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shiqiang Du
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jinmei Song
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Kaiwu Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shiqiang Du.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yu, Y., Liu, B., Du, S. et al. Semi-supervised Multi-view Clustering Based on Non-negative Matrix Factorization and Low-Rank Tensor Representation. Neural Process Lett 55, 7273–7292 (2023). https://doi.org/10.1007/s11063-023-11260-x

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-023-11260-x

Keywords

Search

Navigation